That strike came in his first start in more than three weeks at Peterborough in a performance manager Terry Skiverton described as "outstanding".
"We've had a glimpse of what he can do," Skiverton told BBC Somerset.
"We are looking to do something with him for next year.
"Hopefully it hasn't been too much of a negative for him being out of the side. I've explained the reasons."
Tutte has made City's first-team squad only once, when he sat on the bench in an FA Cup third-round victory over Middlesbrough in 2010.
Source: BBC Sport
Source: BBC Sport